Abstract: This article develops a new Lyapunov design based cooperative attitude control scheme for satellite formation flying with time-varying delay by explicitly taking attitude tracking performance into account. First, this article introduces a proper Lyapunov function to design an adaptive variable structure control law, with this control law the model uncertainties, external disturbances and even variable time-delay in the inter-satellite communication are explicitly considered simultaneously. Second, the tracking performance is evaluated by L₂-gain from the disturbance input to the penalty output. The novelty of the approach lies in the strategy to construct such a Lyapunov function scarifying the L₂-gain dissipative inequation that ensures not only the stability of a cooperative attitude tracking formation system but also an L₂-gain constraint on the tracking performance. This provides a better closed-form solution to depress the external disturbances in order to achieve a better output performance for satellite formation flying cooperative attitude control as compared with the conventional methods. Complete stability and performance analysis is presented and illustrative simulation results of an application to satellite formation flying show that high precision attitude control with zero steady-error is successfully achieved using various scenarios of time-delay.

Key words: formation flying, cooperative control, L₂-gain disturbance attenuation, time delay, Lyapunov function